A linear regression model for quantile function data applied to paired pulmonary 3d CT scans
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913620001030144 |
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| author | Béclin, Marie-Félicia de Micheaux, Pierre Lafaye Molinari, Nicolas Ouimet, Frédéric |
| author_facet | Béclin, Marie-Félicia de Micheaux, Pierre Lafaye Molinari, Nicolas Ouimet, Frédéric |
| contents | This paper introduces a new objective measure for assessing treatment response in asthmatic patients using computed tomography (CT) imaging data. For each patient, CT scans were obtained before and after one year of monoclonal antibody treatment. Following image segmentation, the Hounsfield unit (HU) values of the voxels were encoded through quantile functions. It is hypothesized that patients with improved conditions after treatment will exhibit better expiration, reflected in higher HU values and an upward shift in the quantile curve. To objectively measure treatment response, a novel linear regression model on quantile functions is developed, drawing inspiration from Verde and Irpino (2010). Unlike their framework, the proposed model is parametric and incorporates distributional assumptions on the errors, enabling statistical inference. The model allows for the explicit calculation of regression coefficient estimators and confidence intervals, similar to conventional linear regression. The corresponding data and R code are available on GitHub to facilitate the reproducibility of the analyses presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15049 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A linear regression model for quantile function data applied to paired pulmonary 3d CT scans Béclin, Marie-Félicia de Micheaux, Pierre Lafaye Molinari, Nicolas Ouimet, Frédéric Applications Statistics Theory Computation Methodology 62E15, 62F03, 62J05, 62P10, 62R10 This paper introduces a new objective measure for assessing treatment response in asthmatic patients using computed tomography (CT) imaging data. For each patient, CT scans were obtained before and after one year of monoclonal antibody treatment. Following image segmentation, the Hounsfield unit (HU) values of the voxels were encoded through quantile functions. It is hypothesized that patients with improved conditions after treatment will exhibit better expiration, reflected in higher HU values and an upward shift in the quantile curve. To objectively measure treatment response, a novel linear regression model on quantile functions is developed, drawing inspiration from Verde and Irpino (2010). Unlike their framework, the proposed model is parametric and incorporates distributional assumptions on the errors, enabling statistical inference. The model allows for the explicit calculation of regression coefficient estimators and confidence intervals, similar to conventional linear regression. The corresponding data and R code are available on GitHub to facilitate the reproducibility of the analyses presented. |
| title | A linear regression model for quantile function data applied to paired pulmonary 3d CT scans |
| topic | Applications Statistics Theory Computation Methodology 62E15, 62F03, 62J05, 62P10, 62R10 |
| url | https://arxiv.org/abs/2412.15049 |